Natural extensions for the Rosen fractions
Authors:
Robert M. Burton, Cornelis Kraaikamp and Thomas A. Schmidt
Journal:
Trans. Amer. Math. Soc. 352 (2000), 12771298
MSC (2000):
Primary 11J70, 37A25
Published electronically:
October 15, 1999
MathSciNet review:
1650073
Fulltext PDF Free Access
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Abstract: The Rosen fractions form an infinite family which generalizes the nearestinteger continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.
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 H.C.P. Berbee, Periodicity and absolute regularity, Israel J. Math. 55 (1986), 289304. MR 88b:60088
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 A. Haas and C. Series, Hurwitz constants and Diophantine approximation on Hecke groups, J. London Math. Soc. 34 (1986), 219234. MR 87m:11060
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 H. Jager and C. Kraaikamp, On the approximation by continued fractions, Indag. Math. 51 (1989), 289307. MR 90k:11084
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Additional Information
Robert M. Burton
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email:
burton@math.orst.edu
Cornelis Kraaikamp
Affiliation:
Technische Universiteit Delft & Thomas Stieltjes Institute of Mathematics, ITS (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands
Email:
c.kraaikamp@its.tudelft.nl
Thomas A. Schmidt
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email:
toms@math.orst.edu
DOI:
http://dx.doi.org/10.1090/S0002994799024423
PII:
S 00029947(99)024423
Received by editor(s):
August 1, 1997
Published electronically:
October 15, 1999
Additional Notes:
The first author was partially supported by AFOSR grant 9310275 and NSF grant DMS 9626575. The third author was partially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)
Article copyright:
© Copyright 1999
American Mathematical Society
